# Writing equation of lines in s-intercept Form HELP!!!!!?

please explain how to do these problems, thank you!!
Write the equation of the line that has the given slope and y-intercept
m= 4; b =3
and
m = 2/3 ; b = 6
write the equation of the line that passes through the given point and has the given slope
(6,3) and m = 2
and
(3,3) and m = 1/3
and finally...
Write the equation of the line that passes through the given points
(0,2) and (2,4)
and
( 0,5) and ( 4,17)

+1 vote

The slope m = 4

Y-intercept b = 3

X-intercept a ,Y-intercept b then the equation of the line

X/a + Y/b = 1

Slope  = m = -b/a

Therefore 4 =  -3/a

a = -3/4

substitute the a and b values in the intercept equation

X / (-3/4) + Y/3 =1

-4X / 3 + +Y/3 =1

Multiply each side by 3

-4X + Y = 3

Multiply each side by negative one

4X - Y = -3

Slope m = 2/3

Y-intercept b = 6

The slope is m and Y-intercept b then the equation is Y = mX + c

Substitute the equation m = 2/3 and b = 6

Therefore Y = (2/3)X + 6

Multiply each side by 3

3Y = 3 [(2/3)X +6]

3Y = 2X +18

Therefore 2X -3Y = -18

The equation of hte line passes through the point (X ,Y) and slope m

Y=mX + C

The point is (6 ,3)

m =2

Substitute the equation

3 = 2(6) +  C

3 = 12 + C

C = -9

The equation is Y = 2x - 9

The point is (3 , 3)

Slope m =1/3

Substitute the equation

Therefore 3 = 1/3(3) +C

3 = 1 + C

Therefore C = 3-1

C = 2

m= 1/3

substitute m= 1/3 and c = 2

Y = 1/3X +2

Multiply each side by 3

3Y = X + 6

X - 3Y = -6

The points are (0 ,2) and (2 ,4)

(X1 ,Y1) and (X2 ,Y2) are two points then the slope

m = (Y2 - Y1 ) / (X2 - X1)

Substitute the equaqtion

m = (4-2 )/ (2-0)

m = 2 / 2

Therefore m= 1

The equation form is Y - Y1 = m (X - X1)

Substitue X1 = 0 and Y1 = 2 and m = 1

Therefore Y - 2  = 1 (X - 0)

Y -2 = X

X - Y = -2

The points are (0 , 5) and (4 ,17)

(X1 ,Y1) and (X2 ,Y2) are two points then the slope

m = (Y2 - Y1 ) / (X2 - X1)

Substitute the equaqtion

m = 17- 5 / 4 - 0

m = 12 / 4

Therefore m =3

The equation is Y -Y1 = m (X  - X1)

Substitute the equaqtion

Y - 5 = 3 (X - 0)

Y -5 = 3X

Therefore 3X -Y = -5

Slope - intercept form line equations is y = mx+ b. m is slope and b is y - intercept.
1.
Rreplace m = 4 and b = 3 in slope intercept form equation.
y = 4x + 3
2.
Replace m = 1/3 and b = 6 in slope intercept form equation.
y = 2/3x+6
3.
Replace m = 2 in slope intercept form equation.
y = 2x+ b
Replace (x, y) with (6,3) to find the y-intercept value
3=2* 6 +b
b = 3-12=-9
The equation is y = 2x - 9
4.
Replace m = 1/3 in slope intercept form equation.
y = 1/3x+ b
Replace (x, y) with (3,3) to find the y-intercept value
3=1/3* 3 +b
b = 3-1=2
The equation is y = 1/3x +2
5.
(0,2) and (2,4)
Find the slope m = (y2 - y1)/(x2-x1) = (4-2)/(2-0) = 2/2 = 1
The line equation is y=x+b
Replace (x, y) with (0,2) to find the y-intercept value
2=1* x +b
b = 2
The equation is y = x +2.

(0, 5) and (4, 17)
Find the slope m = (y2 - y1)/(x2 - x1) = (17 - 5)/(4 - 0) = 12/4 = 3
The line equation is y = 3x + b.
Replace (x, y) with (0, 5) to find the y - intercept value.
5 = 3 * 0 +b
b = 5
The equation is y = 3x + 5.